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This study aims to numerically examine the influence of various geometric parameters of a novel W-shaped porous cavity undergoing hybrid nanofluid-based magnetohydrodynamic mixed convection. The W-shaped cavity is modified from the classical trapezoidal cavity by constructing a triangular shape at its bottom. This cavity is isothermally active at the bottom, with different numbers and heights of the triangular peak (or undulation). The heated hybrid nanofluid (Cu–Al₂O₃–H₂O) flow is cooled through the translating top wall. Inclined sidewalls are thermally insulated. To compare the impacts of change in geometric parameters, a square cavity under similar boundary conditions is also simulated. This study is carried out systematically addressing the various influences from a range of parameters like side angles (γ), number (m) and height (λ) of the bottom undulation, Reynolds number (Re), Richardson number (Ri), Darcy number (Da), Hartmann number (Ha), hybrid nanoparticles volume fraction (φ) on the overall thermal performance of the cavity.

Applying the finite volume approach, the transport equations involving multiphysical conditions like porous substance, hybrid nanofluid, magnetic field and shearing force are solved numerically by using a written FORTRAN-based code following the SIMPLE algorithm. The algebraic equations are solved over all the control volumes in an iterative process using the alternate direction implicit scheme and the tri-diagonal matrix algorithm. The converged solution of the iterative process is obtained when the relative error levels satisfy the convergence criterion of 10^–8 and 10^–10 for the maximum residuals and the mass defect, respectively.

It is revealed that an increase in the bottom undulation height always improves the thermal energy transfer despite the reduction of fluid volume. Thermal energy transfer significantly depends on the heating and cooling surface lengths, fluid volume in the cavity and the magnitude of the bottom undulation height of the W-shaped cavity. With the increase in bottom undulation height, effective heating length increases by ∼28%, which leads to a ∼15% reduction in the effective volume of the working fluid and a gain in heat transfer by ∼56.48%. In general, the overall thermal energy transport is improved by increasing Re, Ri and Da; whereas it is suppressed by increasing Ha.

There are many opportunities for future research experimentally or numerically, considering different curvature effects, orientations of the geometry, working fluids, boundary conditions, etc. Furthermore, this study could be extended by considering unsteady flow or turbulent flow.

In many modern systems/processes pertaining to materials processing, continuous casting, food processing, chemical reactors, biomedical applications, etc. fine control in the transport process is a major concern. The findings of this analysis can effectively be useful for other applications for getting more control features in terms of achieving the operational objectives. The approach of the system analysis (considering geometrical size parameters to delve into the underlying transport physics) and the obtained simulated results presented in the work can usefully be applicable to similar thermal systems/devices such as materials processing, thermal mixing, chemical reactors, heat exchangers, etc.

From the well-documented and vast pool of literature survey, it is understood that there exists no such investigation on the considered geometry and study. This study contributes a lot to understanding magnetic field moderated thermofluid flow of a hybrid nanofluid in a porous medium filled W-shaped cavity, in consideration of different geometrical shape parameters (undulation peak numbers at bottom wall, peak heights, side angles and heating and cooling length). Findings brought by this study provide great insights into the design and operation under various ranges of multiphysical thermofluid-flow processing phenomena.

A porous cavity flow field generates entropy owing to energy and momentum exchange within the fluid and at solid barriers. The heat transport and viscosity effects on fluid and solid walls irreversibly generate entropy. This numerical study aims to investigate convective heat transfer together with entropy generation in a partially heated wavy porous cavity filled with a hybrid nanofluid.

The governing equations are nondimensionalized and the domain is transformed into a unit square. A second-order finite difference method is used to have numerical solutions to nondimensional unknowns such as stream function and temperature. This numerical computation is conducted to explore a wide range of regulating parameters, e.g. hybrid nano-particle volume fraction (σ = 0.1%, 0.33%, 0.75%, 1%, 2%), Rayleigh–Darcy number (Ra = 10, 10², 10³), dimensionless length of the heat source (ϵ = 0.25, 0.50,1.0) and amplitude of the wave (a = 0.05, 0.10, 0.15) for a number of undulations (N = 1, 3) per unit length.

A thorough analysis is conducted to analyze the effect of multiple factors such as thermal convective forces, heat source, surface corrugation factors, nanofluid volume fraction and other parameters on entropy generation. The flow and temperature fields are studied through streamlines and isotherms. The average Bejan number suggested that entropy generation is entirely dominated by irreversibility due to heat transport at Ra = 10, and the irreversibility due to the viscosity effect is severe at Ra = 10³, but the increment in s augments irreversibility due to the viscosity effect over the heat transport at Ra = 10².

To the best of the authors’ knowledge, this numerical study, for the first time, analyzes the influence of surface corrugation on the entropy generation related to the cooling of a partial heat source by the convection of a hybrid nanofluid.

The purpose of this paper is to investigate the effects of gravitational modulation on natural convection in a square inclined porous cavity filled by a fluid containing copper nanoparticles.

The present study uses a system of equations that couple hydrodynamics to heat transfer, representing the governing equations of fluid flow in a square domain. The Boussinesq–Darcy flow with Cu-water nanofluid is considered. The dimensionless partial differential equations are solved numerically using finite difference method based on alternating direction implicit scheme. The cavity is differentially heated by constant heat flux, while the top and bottom walls are insulated. The authors examined the effects of gravity amplitude (λ), vibration frequency (σ), tilt angle (α) and Rayleigh number (Ra) on flow and temperature.

The numerical simulations, in the form of streamlines, isotherms, Nusselt number and maximum stream function for different values of amplitude, frequency, tilt angle and Rayleigh number, have revealed an oscillatory behavior in the development of flow and temperature under gravity modulation. An increase of amplitude from 0.5 to 1 intensifies the flow stream (from |ψ_max| = 21.415 to |ψ_max| = 25.262) and improves heat transfer (from Nu¯ = 17.592 to Nu¯ = 20.421). Low-frequency vibration below 50 has a significant impact on the flow and thermal distributions. However, once this threshold is exceeded, the flow weakens, leading to a gradual decrease in heat transfer rate. The inclination angle is an effective parameter for controlling the flow and temperature characteristics. Thus, transitioning the tilt angle from 30° to 60° can increase the flow velocity (from 22.283 to 23.288) while reducing the Nusselt number (from 16.603 to 13.874). Therefore, by manipulating the combination of vibration and inclination, it is founded that for a fixed frequency value of σ = 100 and for increased amplitude (from 0.5 to 1), the flow intensity at inclination of 60° is boosted, and an increase of the heat transfer rate at inclination of 30° is also observed. Convective thermal instabilities may arise depending on the different key factors.

To the best of the authors’ knowledge, this study is original in its examination of the combined effects of modulated gravity and cavity inclination on free convection in nanofluid porous media. It highlights the crucial roles of these two important factors in influencing flow and heat transfer properties.

The main purpose of this study is to analyze the heat transfer phenomena in a dynamically bulging enclosure filled with Cu-water nanofluid. This study examines the convective heat transfer process induced by a bulging area considered a heat source, with the enclosure's side walls having a low temperature and top and bottom walls being treated as adiabatic. Various factors, such as the Rayleigh number (Ra), nanoparticle volume fraction, Darcy effects, Hartmann number (Ha) and effects of magnetic inclination, are analyzed for their impact on the flow behavior and temperature distribution.

The finite element method (FEM) is employed for simulating variations in flow and temperature after validating the results. Solving the non-linear partial differential equations while incorporating the modified Darcy number (10⁻³ ≤ Da ≤ 10⁻¹), Ra (10³ ≤ Ra ≤ 10⁵) and Ha (0 ≤ Ha ≤ 100) as the dimensionless operational parameters.

This study demonstrates that in enclosures with dynamically positioned bulges filled with Cu-water nanofluid, heat transfer is significantly influenced by the bulge location and nanoparticle volume fraction, which alter flow and heat patterns. The varying impact of magnetic fields on heat transfer depends on the Rayleigh and Has.

The geometry configurations employed in this research have broad applications in various engineering disciplines, including heat exchangers, energy storage, biomedical systems and food processing.

This research provides insights into how different shapes of the heated bulging area impact the hydromagnetic convection of Cu-water nanofluid flow in a dynamically bulging-shaped porous system, encompassing curved surfaces and various multi-physical conditions.

The purpose of this paper is to examine numerically the magnetohydrodynamic (MHD) free convection and thermal radiation heat transfer of single walled carbon nanotubes-water nanofluid within T-inverted shaped corrugated cavity comprising porous media including uniform heat source/sink for solar energy power plants applications.

The two-dimensional numerical simulation is performed by drawing on Comsol Multiphysics program, based on the finite element process.

The important results obtained show that increasing numbers of Rayleigh and Darcy and the parameter of radiation enhance the flow of convection heat. Furthermore, by increasing the corrugation height, the convection flow increases, but it decreases with the multiplication of the corrugation height. The use of a flat cavity provides better output than a corrugated cavity.

The role of surface corrugation parameters on the efficiency of free convection and heat transfer of thermal radiation within the porous media containing the T-inverted corrugated cavity including uniform heat source/sink under the impact of Lorentz forces has never been explored. A contrast is also established between a flat cavity and a corrugated one.

The purpose of this study is to investigate the influence of enclosure shape on magnetohydrodynamic (MHD) nanofluidic flow, heat transfer and irreversibility in square, trapezoidal and triangular thermal systems under fluid volume constraints, with the aim of optimizing thermal behavior in diverse applications.

The study uses numerical simulations based on a finite element-based technique to analyze the effects of the Rayleigh number (Ra), Hartmann number (Ha), magnetic field orientation (γ) and nanoparticle concentration (ζ) on heat transfer characteristics and thermodynamic entropy production.

The key findings reveal that the geometrical design significantly influences fluid velocity, heat transfer and irreversibility. Trapezoidal thermal systems outperform square systems, while triangular systems achieve optimal enhancement. Nanoparticle concentration enhances heat transfer and flow strength at higher Rayleigh numbers. The magnetic field intensity has a significant impact on fluid flow and heat transport in natural convection, with higher Hartmann numbers resulting in reduced flow strength and heat transfer. The study also highlights the influence of various parameters on thermodynamic entropy production.

Further research can explore additional geometries, parameters and boundary conditions to expand the understanding of enclosure shape effects on MHD nanofluidic flow and heat transfer. Experimental validation can complement the numerical simulations presented in this study.

This study provides valuable insights into the impact of enclosure shape on heat transfer performance in MHD nanofluid flow systems. The findings contribute to the optimization of thermal behavior in applications such as electronics cooling and energy systems. The comparison of different enclosure shapes and the analysis of thermodynamic entropy production add novelty to the study.

The purpose of this study is to carry out a comprehensive analysis of magneto-hydrodynamics (MHD), nanofluidic flow dynamics and heat transfer as well as thermodynamic irreversibility, within a novel butterfly-shaped cavity. Gaining a thorough understanding of these phenomena will help to facilitate the design and optimization of thermal systems with complex geometries under magnetic fields in diverse applications.

To achieve the objective, the finite element method is used to solve the governing equations of the problem. The effects of various controlling parameters such as butterfly-shaped triangle vertex angle (T), Rayleigh number (Ra), Hartmann number (Ha) and magnetic field inclination angle (γ ) on the hydrothermal performance are analyzed meticulously. By investigating the effects of these parameters, the authors contribute to the existing knowledge by shedding light on their influence on heat and fluid transport within butterfly-shaped cavities.

The major findings of this study reveal that the geometrical shape significantly alters fluid motion, heat transfer and irreversibility production. Maximum heat transfer, as well as entropy generation, occurs when the Rayleigh number reaches its maximum, the Hartmann number is minimized and the angle of the magnetic field is set to 30° or 150°, while the butterfly wings angle or vertex angle is kept at a maximum of 120°. The intensity of the magnetic field significantly controls the heat flow dynamics, with higher magnetic field strength causing a reduction in the flow strength as well as heat transfer. This configuration optimizes the heat transfer characteristics in the system.

Further research can be expanded on this study by examining thermal performance under different curvature effects, orientations, boundary conditions and additional factors. This can be accomplished through numerical simulations or experimental investigations under various multiphysical scenarios.

The geometric configurations explored in this research have practical applications in various engineering fields, including heat exchangers, crystallization processes, microelectronic devices, energy storage systems, mixing processes, food processing, air-conditioning, filtration and more.

This study brings value by exploring a novel geometric configuration comprising the nanofluidic flow, and MHD effect, providing insights and potential innovations in the field of thermal fluid dynamics. The findings contribute a lot toward maximizing thermal performance in diverse fields of applications. The comparison of different hydrothermal behavior and thermodynamic entropy production under the varying geometric configuration adds novelty to this study.

This study aims to numerically investigate heat transport in a trapezoidal cavity using hybrid nanoparticles (Ag-$Al_2O_3$). Unlike previous studies, this one covers magnetohydrodynamics, joule heating with viscous dissipation, heat absorption and generation. The left and right sides of the chasm are frigid. The upper wall heats, whereas the bottom wall remains adiabatic.

After reducing the system of dimensional equations to dimensionless equations, the authors use the Galerkin finite element method to solve them numerically. Geometric parameters affect heating efficiency; thus, the authors use flow metrics such as the Reynold number Re, magnetic parameter M, volume fraction coefficient, heat absorption and Eckert number Ec. The authors use the finite volume method to solve the governing equations after converting them to dimensionless form. The authors also try the artificial neural network method to predict the innovative cavity’s heat response in future scenarios. Transition state charts, regression analysis, MSE and error histograms accelerate, smooth and accurately converge solutions.

As the magnetic parameter and Eckert number increase, the enclosure emits more heat. As Reynold and volume fraction coefficients rise, the Nusselt number falls. It rose as magnetic, Eckert and heat absorption characteristics increased. The average Nusselt number rises with Reynolds and volume fraction coefficients. The magnetic, Eckert and heat absorption characteristics have inverse values.

This study numerically investigates heat transport in a trapezoidal cavity using hybrid nanoparticles (Ag-$Al_2O_3$). Unlike previous studies, this one covers MHD, joule heating with viscous dissipation, heat absorption and generation. The left and right sides of the chasm are frigid. The upper wall heats, whereas the bottom wall remains adiabatic.

This study aims to delve into the coupled mixed convective heat transport process within a grooved channel cavity using CuO-water nanofluid and an inclined magnetic field. The cavity undergoes isothermal heating from the bottom, with variations in the positions of heated walls across the grooved channel. The aim is to assess the impact of heater positions on thermal performance and identify the most effective configuration.

Numerical solutions to the evolved transport equations are obtained using a finite volume method-based indigenous solver. The dimensionless parameters of Reynolds number (1 ≤ Re ≤ 500), Richardson number (0.1 ≤ Ri ≤ 100), Hartmann number (0 ≤ Ha ≤ 70) and magnetic field inclination angle (0° ≤ γ ≤ 180°) are considered. The solved variables generate both local and global variables after discretization using the semi-implicit method for pressure linked equations algorithm on nonuniform grids.

The study reveals that optimal heat transfer occurs when the heater is positioned at the right corner of the grooved cavity. Heat transfer augmentation ranges from 0.5% to 168.53% for Re = 50 to 300 compared to the bottom-heated case. The magnetic field’s orientation significantly influences the average heat transfer, initially rising and then declining with increasing inclination angle. Overall, this analysis underscores the effectiveness of heater positions in achieving superior thermal performance in a grooved channel cavity.

This concept can be extended to explore enhanced thermal performance under various thermal boundary conditions, considering wall curvature effects, different geometry orientations and the presence of porous structures, either numerically or experimentally.

The findings are applicable across diverse fields, including biomedical systems, heat exchanging devices, electronic cooling systems, food processing, drying processes, crystallization, mixing processes and beyond.

This work provides a novel exploration of CuO-water nanofluid flow in mixed convection within a grooved channel cavity under the influence of an inclined magnetic field. The influence of different heater positions on thermomagnetic convection in such a cavity has not been extensively investigated before, contributing to the originality and value of this research.

This study aims to analyze entropy generation and magnetohydrodynamic (MHD) natural convection of hybrid nanofluid in a square cavity, with a heated elliptical block placed at the center, in presence of a periodic-variable magnetic field.

In this paper, simulations were performed with a FORTRAN home code. The numerical methodology used to solve Navier–Stokes, energy and entropy generation equations with corresponding boundary conditions, is essentially based on the finite volume method and full multigrid acceleration.

The cavity is filled with Ag–Tio₂/Water hybrid nanofluid. The main objective of this investigation is to predict the effects of body’s size (6 cases), type of applied magnetic field (variable or uniform), the non-dimensional period number of the variable magnetic field (VMF) (0.2 ≤ Λ ≤ 0.8), the inclination angle of the VMF (0 ≤ χ ≤ 90), Rayleigh number (5 × 103 ≤ Ra ≥ 105) and Hartmann number (5 ≤ Ha ≥ 100) on thermal performance, heat transfer rate, entropy generation and flow patterns.

To the authors’ best knowledge, this paper is the first numerical investigation deals with the entropy generation and natural convection of hybrid nanofluid in a two-dimensional cavity, with specific thermal boundary conditions, containing an elliptical block under periodic-variable magnetic field. Different combinations between flow-governing parameters were made to find optimal thermal performance.